I don't know if anyone is leaving fruits out entirely, but I do know several of the paleo programs recommend going easy on both fruits and nuts if you are wanting to lose weight.
I actually find that I do better with occasional fruits and starchy veggies (like sweet potato or winter squash) but only if there is no alcohol and its occasional or portion controlled. Its easy to overeat both fruit and nuts.

I did it for a long time, but I didn't lose any weight. I think it contributed to the stress I was already under...maybe increased my cortisol output?? Anyway, I've lowered stress and increased carbs and my weight dropped 7 lbs...I also started exercising by lifting weights.

My nutrition is pretty close to Paleo though I eat a few things not allowed on that plan (Smucker's peanut butter, coffee, tea) & leave out some things it includes.

I just sort of stopped eating fruit sometime last year. Not sure why. I normally include LC fruits but I figure organic/pesticide-free fruit is expensive so if I don't miss it why spend money on it.

I'm eating protein, veggies & healthy fats (mostly virgin coconut oil). I do not eat any starchy veggies or carbs. I use flax meal on occasion but I don't miss bread-type foods at all so it is a rare occasion.

I eat no fruit some days, minimal low carb fruit more as a condiment on my salad other days (blueberries/kiwi/strawberries). I eliminated nightshades as they can be inflammatory. I am doing high fat, moderate protein paleo lc. I want to be in ketosis as I'm wanting to knock out some cancer cells.

I'm doing Primal low carb. I just came back to low carb this week to knock off a stubborn last 5-10 before the holidays. I'm in the "craving" stage right now. Once ketosis kicks in, I will feel better. I'm a sugar junkie so fruit sets up cravings for more.

I've done Paleo, Whole 75 last spring. But right now I'm having some dairy.